Evolution of the magnetic and structural properties of Fe$_{1-x}$Co$_x$V$_2$O$_4$

The magnetic and structural properties of single crystal Fe$_{1-x}$Co$_x$V$_2$O$_{4}$ samples have been investigated by performing specific heat, susceptibility, neutron diffraction, and X-ray diffraction measurements. As the orbital-active Fe$^{2+}$ ions with larger ionic size are gradually substituted by the orbital-inactive Co$^{2+}$ ions with smaller ionic size, the system approaches the itinerant electron limit with decreasing V-V distance. Then, various factors such as the Jahn-Teller distortion and the spin-orbital coupling of the Fe$^{2+}$ ions on the A sites and the orbital ordering and electronic itinerancy of the V$^{3+}$ ions on the B sites compete with each other to produce a complex magnetic and structural phase diagram. This phase diagram is compared to those of Fe$_{1-x}$Mn$_x$V$_2$O$_{4}$ and Mn$_{1-x}$Co$_x$V$_2$O$_{4}$ to emphasize several distinct features.